2015/06/20 by Irina Gelbukh, Gelbukh, Irina
Mathematics · #14F35 #57N65 #57R30 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:14F35 #msc:57N65 #msc:57R30
paper · pdf · doi:10.48550/arxiv.1506.06300
Accepted to Mathematica Slovaca, 2015
arxiv created 2015/06/20 · arxiv updated 2015/06/23
We study b'1(M), the co-rank of the fundamental group of a smooth closed connected manifold M. We calculate this value for the direct product of manifolds. We characterize the set of all possible combinations of b'1(M) and the first Betti number b1(M) by explicitly constructing manifolds with any possible combination of b'1(M) and b1(M) in any given dimension. Finally, we apply our results to the topology of Morse form foliations. In particular, we construct a manifold M and a Morse form ω on it for any possible combination of b'1(M), b1(M), m(ω), and c(ω), where m(ω) is the number of minimal components and c(ω) is the maximum number of homologically independent compact leaves of ω.